A chirp is characterized by a frequency that is swept across a spectrum. The sweep can be of a first or higher order. When it is of the first order, the signal is a linear chirp. If it is second order, then the signal is a quadratic chirp and so on. Chirps do not lend themselves to analysis via classical Fourier transform techniques like the fast Fourier transform (FFT). The FFT is a proper tool to analyze signals with invariant or slowly varying frequencies over an observation interval. Analyzing signals with time-varying frequencies, however, requires a different set of tools.
A Short-Time Fourier Transform (STFT) is well suited and widely used for analyzing signals with time-varying frequencies. Even with STFT, however, analyzing a time-frequency spectrum like that of FIG. 5 for a chirp or for spectral features indicative of a chirp is arduous. What may be visually obvious, however, is not as easily attained algorithmically. Beside the fact that a chirp detecting algorithm has to perform a two-dimensional search of the entire spectrum, the algorithm has to make decisions as to what is a chirp or what is indicative of a chirp on a large number of pixels (i.e., spectral information or data). It seems advantageous to analyze a signal in a transform domain where a chirp is a localized signal rather than one that is distributed across the entire spectrum.
Academic work in the signal processing has produced several algorithms that are designed to detect or estimate chirps in a localized manner. The work includes a maximum likelihood technique, Discrete Chirp Fourier transform, and the cubic phase transform. These techniques, however, are limited to signals having a single chirp present, and a noise model that is additive and Gaussian in nature. These techniques are inadequate for detecting or estimating chirps in signals containing multiple chirps and having noise that is multiplicative in nature.
Particularly challenging is the presence of broadband noise that can clutter the entire spectrum. By comparison, a chirp occupies a finite region across frequency. Broadband noise has a spectral signature that spreads energy across the entire spectrum. This type of noise may be uniform across frequency but its time spread extends for the duration of the noise burst in the time domain signal.